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Contact Mechanics and Elements of Tribology 5Pt Foreword Contact Mechanics and Elements of Tribology Foreword Vladislav A. Yastrebov MINES ParisTech, PSL Research University, Centre des Matériaux, CNRS UMR 7633, Evry, France @ Centre des Matériaux February 8, 2016 Outline Acquaintance Questionnaire Course content Historical remark Complexity Notations Questionnaire Please fill in the questionnaire Message to DMS students : Rank all suggested topics1 for your report in the order of decreasing attractiveness Before the lunch one topic will be assigned to everybody On Friday (12/02) you will have 10 minutes to present briefly your topic to other students If you are not a DMS student but would like to follow, you are welcome Basava, Andrei and Paolo will also present rapidly their research projects on 12/02 By Friday (19/02) you will need to send me your report on your topic ( 10 pages in Français/English) ≈ Criteria of evaluation : no plagiarism, scientifically sound report 1or suggest a different one but not related to your master project V.A. Yastrebov 3/10 Course content Lectures : 1 Motivation : industrial applications 2 Contact Mechanics I & II 3 Contact at small scales : surface roughness 4 Computational Contact Mechanics 5 Contact rheology & friction laws 6 Elements of tribology : friction, adhesion, wear 7 Wear and fretting (by Henry Proudhon) 8 Multiphysical problems in contact 9 Your presentations V.A. Yastrebov 4/10 Course content Lectures : 1 Motivation : industrial applications 2 Contact Mechanics I & II 3 Contact at small scales : surface roughness 4 Computational Contact Mechanics 5 Contact rheology & friction laws 6 Elements of tribology : friction, adhesion, wear 7 Wear and fretting (by Henry Proudhon) 8 Multiphysical problems in contact 9 Your presentations Practice : 1 Chalk and blackboard : Boussinesq, Cerruti, Flamant 2 Chalk and blackboard : Hertz contact 3 Computer : rough contact 4 Computer : frictionless and frictional cylindrical contact 5 Computer : elasto-plastic spherical indentation V.A. Yastrebov 5/10 Historical remark Use of friction and overcoming of friction Frictional heat - lighting of fire > 40 000 years ago. Ancient Egypt - lubrication of surfaces with oil > 5 000 years ago. V.A. Yastrebov 6/10 Historical remark First scientific studies on contact and friction Leonardo da Vinci [1452-1519] first friction laws and many other tribological topics Isaac Newton [1687] From Leonardo da Vinci’s notebook Newton’s third law for bodies interaction Guillaume Amontons [1699] rediscovered friction laws Leonhard Euler [1707-1783] roughness theory of friction Roughness theory of friction V.A. Yastrebov 7/10 Historical remark First scientific studies on contact and friction Charles-Augustin de Coulomb [1789] friction independence on sliding velocity and roughness, the influence of the time of repose Heinrich Hertz [1881-1882] Photoelasticity analysis of Hertz contact problem the first study on contact of (fringes correspond to max shear stresses) deformable solids Holm [1938], Ernst and Merchant [1940], Bowden and Tabor [1942] difference between apparent and real contact areas, adhesion theory. Apparent and real areas of contact V.A. Yastrebov 8/10 Complexity Zoom on the contact interface Between different heterogeneous materials with specific rough surfaces Under various loads V.A. Yastrebov 9/10 Involved physical phenomena Primary phenomena (atomic / electronic interactions) 1 Contact (non-penetration) 2 Friction (tangential resistance) 3 Adhesion (resistance to tension) 4 Surface energy 5 Quantum effects (tunneling, Casimir effect) Secondary phenomena 1 Wear 2 Lubrication (fluid-structure interaction) 3 Environmental effects (oxidation) 4 Aging, diffusion 5 Heat production 6 Heat and electricity transfer V.A. Yastrebov 10/10 Contact complexity : physics and mathematics Particular difficulties related to contact problems : multiphysical aspects, mathematical aspects Fractality of surfaces Interface chemistry Hardly accessible contact interface Generation and diffusion of heat Multiscale and multiphysical nature of friction V.A. Yastrebov 11/10 Contact complexity : physics and mathematics Particular difficulties related to contact problems : multiphysical aspects, mathematical aspects One of the most hard problems in mechanics Lack of standard optimization problem Non-convexity and non-differentiability Non-continuous character Bad scalability V.A. Yastrebov 12/10 Notations Vectors and tensors a; α scalars a b = c scalar (dot) product • • · b vectors a b = c vector (cross) product • • × C; β 2nd order tensors a b = C tensor product • = = • ⊗ = 4 D 4th order tensors AT transposition • = • = a = B gradient operator a = c divergence operator •r = •r· a = B rotor operator I = e e unitary 2nd order tensor •r× = •= i ⊗ i Mechanics σ Cauchy stress tensor " Small strain tensor • = • = g; gn gap, normal gap ξ position vector in parent space • • penalty parameter n∼ outward unit normal vector • • @% @% λ, λn; λt lagrange multipliers ; surface tangent vectors • • ∂ξ1 ∂ξ2 σn =(σ n) n contact pressure f Coefficient of friction • =· · • V.A. Yastrebov 13/10 Welcome to CMET course ! ,.
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